Replay a bounded DR25 parent sample

Start from the searched stars

The stellar parent is the author’s earlier Gaia-updated tutorial K-star catalog at commit 5eda15caeb3ba6204b34a4e9975738b527e3704d. It contains 16,107 stars. It is not the later Berger 2020 baseline used in another occurrence analysis. Preserve that distinction before comparing any published rates.

The complete official INJ1 pixel-injection table has 146,294 rows, with decoded SHA-256 beginning 6b9f2d8b5979. Intersect its targets with the fixed parent to obtain 12,363 stars. The remaining 3,744 parent stars have no matching INJ1 trial and are outside the inferred population. Within the intersection, 517 candidates occupy 378 hosts; 11,985 searched stars have no candidate.

The author’s thirty-percent cadence-loss cut is part of this parent definition. A stricter five-percent cut changes both the stars and candidate population. It cannot be treated as an extra uncertainty bar on the original population. The delivered accounting preserves this example.

Reading: A Probabilistic Approach to Kepler Completeness and Reliability for Exoplanet Occurrence Rates · NASA Exoplanet Archive DR25 completeness/reliability and simulated products

Read an injection as an experiment

Open the literal IPAC header before converting columns. Period is in days; epoch is BKJD, defined as BJD minus 2454833. Depth is in parts per million after source aperture corrections; duration is in hours. The valid-transit count is weighted and can be fractional. Do not round it into a three-transit gate.

Join recovered signals by their exact TCE identifier to the complete 45,377-row INJ1 Robovetter table. A recovered signal can still receive a false-positive disposition. A missing join stops the program instead of becoming a silent success or failure.

The source prose describes successful ephemeris matching that permits half/double and third/triple periods. The actual file also contains recovery code 2, although its short flag description lists only 0 and 1. The retained code 2 PC rows have the corresponding harmonic periods. Count these recognized matches as successful planet recovery and keep their count separately. The earlier same-period-only calculation remains a definition sensitivity.

Across the whole selected parent there are 4,049 same-period PC matches and 27 alias-PC matches. The response-training domain, ten to one hundred days with source duration 1.5–15 hours, contains 2,202 trials: 914 same-period successes and 3 alias successes. Failures remain in the Bernoulli likelihood.

Reading: Christiansen 2017, Pixel-Level Transit Injection Tests of Pipeline Detection Efficiency for DR25 · Coughlin, Robovetter Completeness and Effectiveness for DR25

Fit a response and test stars it has not seen

The signal proxy divides the aperture-corrected source depth by the measured robust CDPP interpolated logarithmically at the source duration, then multiplies by the square root of the expected post-cut exposure span divided by period. It is an approximate feature, not the source’s expected MES. No second observing-window factor is applied to the empirical final recovery.

The first pooled response had plausible overall calibration but whole-target held-out magnitude-group residuals about positive six and negative four-and-a-half standard deviations. Those failures are retained. The refined model shifts the transition with stellar magnitude as well as period. Splits are assigned by a hash of the target identity, so a target’s data cannot leak across its training and test groups.

The amplitude mapping for a hypothetical planet uses one fixed target-specific scale: source injected depth divided by the four-coefficient finite-disk depth at its source radius ratio and impact parameter. This scale is not identified as pure crowding. An unanchored relation is saved as a separate sensitivity. The supplied stellar intensity profiles stay positive over the checked disk. The scale’s median is $1.246$, with each target retaining its own value.

A source-MES sensitivity refits the response using the supplied corrected Expected_MES, then transfers a hypothetical planet from each target’s reference signal. The final proxy exceeds source MES by a median factor $1.229$ in the 2,202 training trials. An earlier linear-CDPP, weighted-transit-count proxy had median ratio $1.315$ under different filters. These feature definitions remain separate. The MES condition leaves 444 targets without a usable source-duration anchor inside measured CDPP support; their recovery stays unknown. Its supported exposure median is about $236$ and upper rate-family median about $0.323$. Target-held-out recovery checks use supplied source features; they do not independently validate a new physical-radius-to-signal relation.

The refined posterior has proper priors, including a Beta prior for the plateau and Gaussian priors for the transformed width and signed slopes. Eight chains retain 24,000 positions each after 5,000 discarded adaptation steps. Rank/folded split diagnostics and effective sample sizes use the full retained chains. An independent full-support Student-t importance integral checks posterior moments and integration refinement.

Reading: Burke and Catanzarite 2017, Per-Target Detection Contours for DR25 · Measuring Transit Signal Recovery in the Kepler Pipeline IV

Carry the unknown response into the rate

The original stored radius convention puts 80 candidates in the chosen region. Recomputing from the supplied transit radius ratio and stellar radius with declared nominal conversion constants gives 79. Preserve both columns and counts. Do not silently replace one definition with the other.

Every searched star contributes to the exposure integral over ten to thirty days and two to four nominal Earth radii. The assumed shape is uniform in logarithmic period and radius. Within empirical duration, proxy and magnitude support, use the fitted response. Outside that support, and in the finite-radius grazing shell not sampled by the source injections, allow recovery anywhere from zero to one.

The unidentified geometric exposure is about 162 effective stars. Its two endpoints are actually propagated through normalized integer-catalog Gamma mixtures, with the external classification probabilities fixed. The posterior median ranges approximately from 0.205 to 0.362 planet per searched star. The outer 95-percent envelope is approximately 0.162 to 0.450.

These are conditions on the same restricted population, not a single probability law over the unknown response. The envelope is not a unique 95-percent posterior interval. Population-shape errors, response-model mismatch and K-star false-alarm uncertainty still need separate models.

Reading: A Probabilistic Approach to Kepler Completeness and Reliability for Exoplanet Occurrence Rates · IAU 2015 Resolution B3 nominal conversion constants

Move stellar radii and rerun both sides

A coherent one-reported-sigma upward stellar-radius shift changes the nominal candidate count from 79 to 84; the downward shift gives 74. Every planet around the same star moves with that host. The same shifted stellar radii enter geometry and predicted signal before the exposure is recalculated.

The rate-family upper median is about 0.323 for the upward shift and 0.412 for the downward shift. These are sensitivity cases, not posterior draws from a fully specified stellar/transit covariance. The source does not supply that covariance. Additional scripts preserve the stricter cadence parent, radius-convention difference, retired pooled response, short-duration feature failure and alias definition.

Reading: Shallower radius valley around low-mass hosts · Reliability Correction is Key for Robust Kepler Occurrence Rates

Run the independent folder

The public ZIP contains the standalone science scripts, NASA inputs with their attribution, numerical references and the synthetic offline example. The earlier author tutorial repository has no identified license in the fixed tree. The public ZIP supplies a named retrieval script and source metadata. Two fixed author URLs supply the stellar ZIP and candidate table.

The first author-input transfer totals about 4.42 MB and checks complete byte counts and SHA-256 before accepting either file. After obtaining those sources and installing the declared dependencies, the real exercise runs offline. Its receipt distinguishes a new HTTP response from a previously verified local cache.

Run the source checks before fitting. Recompute the response, then the finite-support exposure, then the occurrence family. The output checker verifies target counts, priors, diagnostic thresholds and numerical tolerances. Use chain diagnostics and the independent posterior integral to assess exploration; use hashes to check file identity.

python3 verify_inputs.py .
python3 offline_checks.py --out rerun-offline.json
python3 fetch_author_inputs.py input
python3 replay.py --inputs input --out-dir rerun --sensitivities
python3 verify_outputs.py --expected expected --actual rerun

Reading: NASA Exoplanet Archive reuse and acknowledgment guidance

Use the result for its stated population

This two-to-four-radius slice does not measure the full radius valley. The next guide reads the published valley distributions and their different selected stellar populations. The synthetic experiment separately supplies a known smooth distribution and a known bimodal distribution, so you can see selection and radius uncertainty operate before interpreting a physical gap.

For the next occurrence study, first write down the searched stars, the planet region, the within-region shape, the final detection definition, the classification model and every uncalibrated region. Those choices determine which population the number describes.

Reading: The California-Kepler Survey III. A Gap in the Radius Distribution of Small Planets · About 30 percent of Sun-like Stars Have Kepler-like Planetary Systems